F(2a)=2/2a+2

Solution for F(2a)=2/2a+2 equation:

(2F)=2/2F+2

We move all terms to the left:

(2F)-(2/2F+2)=0


Domain of the equation: 2F+2)!=0

F∈R


We get rid of parentheses

2F-2/2F-2=0

We multiply all the terms by the denominator


2F*2F-2*2F-2=0

Wy multiply elements

4F^2-4F-2=0

a = 4; b = -4; c = -2;
Δ = b2-4ac
Δ = -42-4·4·(-2)
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{3}}{2*4}=\frac{4-4\sqrt{3}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{3}}{2*4}=\frac{4+4\sqrt{3}}{8}
$